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Goryan [66]
3 years ago
14

Is the equation y=2x a function

Mathematics
2 answers:
Leto [7]3 years ago
7 0

Answer:

Yes it is a function

Step-by-step explanation:


soldier1979 [14.2K]3 years ago
3 0

Yes. It's a linear function.

<u>x | y</u>

<u>0| 2(0) = 0</u>

<u>1| 2(1) = 2</u>

<u>2| 2(2) = 4</u>

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Find all the solutions for the equation:
Contact [7]

2y^2\,\mathrm dx-(x+y)^2\,\mathrm dy=0

Divide both sides by x^2\,\mathrm dx to get

2\left(\dfrac yx\right)^2-\left(1+\dfrac yx\right)^2\dfrac{\mathrm dy}{\mathrm dx}=0

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2\left(\frac yx\right)^2}{\left(1+\frac yx\right)^2}

Substitute v(x)=\dfrac{y(x)}x, so that \dfrac{\mathrm dv(x)}{\mathrm dx}=\dfrac{x\frac{\mathrm dy(x)}{\mathrm dx}-y(x)}{x^2}. Then

x\dfrac{\mathrm dv}{\mathrm dx}+v=\dfrac{2v^2}{(1+v)^2}

x\dfrac{\mathrm dv}{\mathrm dx}=\dfrac{2v^2-v(1+v)^2}{(1+v)^2}

x\dfrac{\mathrm dv}{\mathrm dx}=-\dfrac{v(1+v^2)}{(1+v)^2}

The remaining ODE is separable. Separating the variables gives

\dfrac{(1+v)^2}{v(1+v^2)}\,\mathrm dv=-\dfrac{\mathrm dx}x

Integrate both sides. On the left, split up the integrand into partial fractions.

\dfrac{(1+v)^2}{v(1+v^2)}=\dfrac{v^2+2v+1}{v(v^2+1)}=\dfrac av+\dfrac{bv+c}{v^2+1}

\implies v^2+2v+1=a(v^2+1)+(bv+c)v

\implies v^2+2v+1=(a+b)v^2+cv+a

\implies a=1,b=0,c=2

Then

\displaystyle\int\frac{(1+v)^2}{v(1+v^2)}\,\mathrm dv=\int\left(\frac1v+\frac2{v^2+1}\right)\,\mathrm dv=\ln|v|+2\tan^{-1}v

On the right, we have

\displaystyle-\int\frac{\mathrm dx}x=-\ln|x|+C

Solving for v(x) explicitly is unlikely to succeed, so we leave the solution in implicit form,

\ln|v(x)|+2\tan^{-1}v(x)=-\ln|x|+C

and finally solve in terms of y(x) by replacing v(x)=\dfrac{y(x)}x:

\ln\left|\frac{y(x)}x\right|+2\tan^{-1}\dfrac{y(x)}x=-\ln|x|+C

\ln|y(x)|-\ln|x|+2\tan^{-1}\dfrac{y(x)}x=-\ln|x|+C

\boxed{\ln|y(x)|+2\tan^{-1}\dfrac{y(x)}x=C}

7 0
3 years ago
a store sells small notebooks for $7 and large notebooks for $14. if a student buys 6 note books for $63, how many notebooks eac
bija089 [108]
The answer is 3 of each.  3X7=21; 14X3=42, and 42+21= 63.
4 0
3 years ago
Read 2 more answers
Asap help.! Circle measurements
Margaret [11]

Answer:

D

Step-by-step explanation:

Here, we want to get the value of x;

To get this, we simply use one of the circle angle and arc properties

Mathematically;

arc MN = 2 * arc MLN

3x + 22 = 134/2

That will be;

3x + 22 = 67

3x = 67-22

3x = 45

x = 45/3

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5 0
3 years ago
Breoz
Viktor [21]

The second statement is:

B: a + b = b + a

Which is the commutative property, so we know that this statement is true.

<h3>Which statement is always true?</h3>

Remember that for integer numbers, we have the following properties:

  • Commutative property: A + B = B + A
  • Associative property: (A + B) + C = A + (B + C)

Now, in this case we know that a and b are integer numbers, first we can see that the second statement is:

B: a + b = b + a

Which is the commutative property, so we know that this statement is true.

The other 3 statements are false. You can see it by evaluating a = 0 and b = 1.

If you want to learn more about addition:

brainly.com/question/25421984

#SPJ1

6 0
11 months ago
Simplify the expression? <br><br><br>-3 <br><br><br>-5<br><br><br>5<br><br><br>9/5
inysia [295]
The simplified expression is 9/5

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3 years ago
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